Two engineers are having an argument about the efficiency of a tube-side multipass heat exchanger compared to a similar exchanger with a single tube-side pass. Smith claims that for a given number of tubes and rate of heat transfer, more area is required in a two-pass exchanger than in a one-pass, because the effective temperature difference is less. Jones, on the other hand, claims that because the tube-side velocity and hence coefficient is higher, less area is required in a two-pass exchanger. With the conditions given below, which engineer is correct? Which case would you recommend, or what changes in the exchanger would you recommend?

Question

Exchanger specifications

– 200 tube passes total

– 1 in.-O.D copper tubes, 16 B.W.G.

Tube-side fluid

Water entering at 16°C, leaving at 28°C, with a rate of 225,000 kg/h.

Shell-side fluid

Mobiltherm 600, entering at 50°C, leaving at 33°C.

Shell side coefficient = 1700 W/(m2 K)

GIVEN

• Tube and shell heat exchanger - water in tubes, Mobiltherm 600 in shell

• Number of tube passes (Np) = 200

• Tubes are 1 in copper 16 B.W.G.

• Water flow rate m w= 225,000 kg/h = 62.5 kg/s

• Water temperatures

? Tw,in = 16°C

? Tw,out = 28°

• Mobiltherm temperatures

? Tm,in = 50°C

? Tm,out = 33°C

• Shell side heat transfer coefficient h o= 1700 W/(m2 K)

FIND

• Which required less transfer area: (a) single tube pass (b) Two tube passes?

ASSUMPTIONS

• Thermal resistance of copper tube wall is negligible

SKETCH



PROPERTIES AND CONSTANTS

for 1 in 16 B.W.G. tubes, the diameters are

Di = 0.870 in. = 0.0221 m

Do = 1.0 in. = 0.0254 m

for water at the average temperature of 22°C

Thermal conductivity (k) = 0.601 W/(m K)

Kinematic viscosity (?) = 0.957 × 10–6 m2/s

Prandtl number (Pr) = 6.6

Density (?) = 998 kg/m3

Specific heat (cpw) = 4180 J/(kg K)

the specific heat of Mobiltherm 600 at its average temperature of 42°C (cpm) = 1654 J/(kg K)

Answer 1

For case (a) number of flow passages (N) = Total passes/(passes per tube) = 200/1 = 200.

For case (b) N = 200/2 = 100.

The water velocity (V) is determined by



The Reynolds number is



The Nusselt number for turbulent flow in a tube is



The overall heat transfer coefficient, neglecting the tube wall resistance is



Case (a)



Case (b)



The Log-mean temperature difference for counterflow, is



For case (a): ?Tmean = LMTD = 19.4°C

For case (b): The LMTD must be corrected



F = 0.91



The rate of heat transfer is



Case (a)



Case (b)



COMMENTS

For these operating conditions, the double-pass heat exchanger requires about 8% less area because although the mean temperature difference for the double pass is 9% less than that for the single pass, the overall heat transfer coefficient is 18% greater.